Proceedings of the Korean Institute of Intelligent Systems Conference (한국지능시스템학회:학술대회논문집)

Korean Institute of Intelligent Systems (한국지능시스템학회)
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Approximation of the smooth functions by using fuzzy systems: A review of the advantages

퍼지 시스템을 이용한 함수표현의 장점; A REVIEW

  • Moon B. S. (Dept. of Instrumentation & Control - Human Factors, Korea Atomic Energy Research Institute) ;
  • Lee J. S. (Dept. of Instrumentation & Control - Human Factors, Korea Atomic Energy Research Institute) ;
  • Lee D. Y. (Dept. of Instrumentation & Control - Human Factors, Korea Atomic Energy Research Institute) ;
  • Kwon K. C. (Dept. of Instrumentation & Control - Human Factors, Korea Atomic Energy Research Institute)
  • Published : 2005.11.01
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Abstract

A review of how the functions of two or more independent variables can be approximated by using fuzzy systems is provided in this paper. We start with an exact represention of a linear interpolation function of two independent variables by using a fuzzy system. Next, we describe how this function can be approximated by another fuzzy system with a lesser number or with a desired number of output fuzzy sets. Thus, a reduction of the storage needed is achieved by storing the fuzzy rules or equivalently the output fuzzy set numbers instead of storing the whole discrete function values. A description on how the cubic spl me interpolation function can be represented exactly by using the fuzzy system method is provided, along with a few examples where fuzzy rule tables with a size of 7$\times$7 provide a representation of the functions with relative errors of the order of $10^{2}$ or less.

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